Notes – Compound Interest Formula and Pert With Logs

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Presentation transcript:

Notes – Compound Interest Formula and Pert With Logs Remember , the formula for continuously compounded interest is: A = Pe(r*t) with A = Amount earned, P = Principle(amount Put in) r = interest rate t = time in years Steps to find r or t: Plug in all values given for A, P, and r OR t into formula. Divide both sides by P.(round to 2 decimal places) Place ln on both sides of = in front of each side. ln and e will cancel out and exponent will come down. Use calculator to find the ln of the number on the left side of the =. 5. Set exponent = to number obtained in step 4 and divide by the number next to r or t on both sides. Ex. Robert has $4200 to invest in an account earning 4% interest, compounded continuously. How many years would he need to invest the money in order to make a total of $5600? Ex. Jane has $6250 to invest in an account earning 5.5% interest, compounded continuously. How many years would she need to invest the money in order to make a total of $10000? Ex. Michael has $8400 to invest in an account compounded continuously for 6 years. What interest rate does he need to get $12600 at the end of the 6 years? Ex. Michelle has $4700 to invest in an account compounded continuously for 8 years. What interest rate does she need to double her money at the end of the 8 years?

Compound Interest Formula and Pert With Logs Practice Solve the following problems for r or t. Show work! Round all answers to 2 decimal places. 7. Delores has $9600 to invest in an account earning 5.5% interest, compounded continuously. How many years would she need to invest the money in order to make a total of $14400? 8. Jeff has $7500 to invest in an account earning 4.5% interest, compounded continuously. How many years would he need to invest the money in order to make a total of $13500? 9. Francis has $8700 to invest in an account earning 6% interest, the money in order to double her money?

Compound Interest Formula and Pert With Logs Practice Solve the following problems for r or t. Show work! Round all answers to 2 decimal places. 10. Tracy has $2700 to invest in an account compounded continuously for 6 years. What interest rate does she need to get $4500 at the end of the 6 years? 11. Allen has $13200 to invest in an account compounded continuously for 8 years. What interest rate does he need to get $21120 at the end of the 8 years? Marion has $13900 to invest in an account compounded continuously for 7years. What interest rate would she need to double her money at the end of the 7 years?

Warmup 12-7 Solve the following equations for x. Show work! Round to 2 decimal places. 1. 2. 3. Condense the following log expression: 4. Expand the following log expression: 5. Find the inverse: 6. Mark has $10800 to invest at 6% interest compounded quarterly. How long would he need to invest the money to earn a total of $14040?

Warmup 12-7 Solve the following equations for x. Show work! Round to 2 decimal places. 1. 2. 3. Condense the following log expression: 4. Expand the following log expression: 5. Find the inverse: 6. Mary has $12000 to invest at 4.75% interest compounded quarterly. How long would she need to invest the money to earn a total of $14400?

Notes –Depreciation Formulas Depreciation Formula: A = P(1 – r)t where A = Amount item is worth P = original value of item r = rate of decrease (converted to a decimal) t = time in years Ex. If a person paid $32000 for a new car, and the car’s value depreciates at a rate of 15% per year, how many years before the car is worth: a. $25000? b. $18000? c. $10000 d. $5000? Ex. If a person paid $1450 for a new computer, and the computer’s value depreciates at a rate of 28% per year, how many years until the computer is worth: a. $1000? b. $725? c. $400? d. $100? Ex. If a person paid $300 for a cell phone, and the phone’s value depreciates at a rate of 12% per year, how many years until the phone is worth: a. $200? b. $150? c. $50?

Depreciation Practice 1. A person bought a car for $35000. The car’s value goes down 16% per year. How many years until the car is worth: a. $25000? b. $17500? c. $10000? d. $5000? 2. A person bought a computer for $875. The computer’s value goes down 26% per year. How many years until the computer is only worth: $600? b. $438? $250? d. $100? 3. A person bought a plasma HDTV for $1500. The value of the TV goes down 24% per year. How many years will it take for the TV to be worth only: $1000? b. $750? c. $450? d $150? 4. A person bought a smart phone for $500. The phone’s value goes down 19% per year. How many years until the phone Is only worth: a. $400? b. $250? c. $100? d. $50?